XIX International Conference on Water Resources CMWR 2012

University of Illinois at Urbana-Champaign June 17-22, 2012

APPLICATION OF 3D NUMERICAL MODELS IN CONFLUENCE HYDRODYNAMICS MODELLING

Dejana Đorđević

University of Belgrade Faculty of Civil Engineering

Bulevar kralja Aleksandra 73, 11000 Belgrade, Serbia e-mail: dejana@grf.bg.ac.rs

Key words: 3D modelling, river confluence, model assessment

Summary. In this paper performance of the SSIIM2 model (3D finite-volume model with the k-ε-type turbulence model closure) in confluence hydrodynamics modelling is assessed using the published experimental data and the author’s field data. It is shown that the transfer of momentum from the tributary to the main channel and variations of the recirculation zone width are modeled satisfactorily, and that the shape of the velocity profiles in the post-confluence channel is captured well. However, velocity magnitudes are underestimated, especially that of the vertical velocity. This may be attributed to the fact that the model is based on the assumption of the hydrostatic pressure distribution, which is not satisfied at the confluence.

1 INTRODUCTION

Flow in a river confluence is three-dimensional due to collision of the combining flows and their interaction with the riverbed. This three-dimensional fluid motion results in complex mixing and transport processes and phenomena. Thus, a river confluence is a perfect example to which a 3D numerical model is reasonable to apply.

Since the quality of the mixing and transport processes prediction highly depends on the ability of the model to reproduce flow and pressure fields correctly, it is of crucial importance to assess numerical model’s performance in confluence hydrodynamics modelling first. There were several attempts to apply and assess 3D models’ performance starting from mid 1990-ies (the PHOENICS1-3 and 3D model with the k-ω type turbulence model closure4). Both laboratory1-2, 4-5 and field data2,6 were used for the assessment. This paper is focused on the application of the SSIIM2 model with two-equation turbulence model closure of k-ε type7 that was already used in various river hydraulics studies.

The paper aims at demonstrating and assessing the model’s performance in confluence hydrodynamics modelling through a series of three examples with the increasing complexity of the confluence planform and riverbed geometries. The paper will concentrate on the comparison of the measured and calculated velocity profiles in different regions of the confluence hydrodynamics zone8 (CHZ). Additionally, where applicable, the size of the recirculation zone (RZ) will be deduced from the experimental data and compared to the size of the simulated zone. Thus, a comprehensive view of the strengths and weaknesses of the model can be gained and directions for the improvement of the model can be identified.

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2 LABORATORY AND FIELD CONFLUENCES

Laboratory confluence in the first example is Shumate’s8 90o confluence of two straight channels with equal bed elevations (concordant beds confluence-CB). In such a confluence a large recirculation zone may be formed downstream of the downstream junction corner. Thus, it allows for the assessment of the model’s ability to predict recirculation zone dimensions and the flow structure within and outside the zone. The plan view is shown in Figure 1a; positions of the measuring cross-sections are indicated in Figure 1b and distribution of the measuring points within the cross-section in the post-confluence channel (PCC) where RZ exists, in Figure 1c. Outside the RZ there were seven equally spaced verticals. The three velocity components (u, v, w) were instantaneously measured in each point using the ADV (Acoustic Doppler Velocimeter) down looking probe. Data from the experiment in which DR = QMR/Qtot = 0.583 (QMR = 0.099m3/s, QT = 0.071 m3/s) were used in this study. Details of the experimental procedure can be found in Shumate8.

Laboratory confluence in the second example is Biron et al.’s9, 10 30o single-flume confluence with a bend in a tributary that was formed by inserting two dividing blocks in 0.30 m wide and 10 m long laboratory flume (Fig. 2c). The model has two layouts – one with equal bed elevations (CB confluence, Fig. 2a) and the other with the tributary channel elevated 0.03 m above the bed of the main channel (discordant beds confluence-DB, Fig. 2b). Only two velocity components (u and w) were measured using the LDA (Laser Doppler Anemometer) two-component probe. Distribution of the measuring verticals is shown in Figure 2c. Simulation details are given in Table 1. Other details regarding the experimental procedure can be found in Biron et al.9, 10. The experiments are suitable for the assessment of the model’s ability to simulate flow in complex planform and riverbed geometries.

Since the width-to-depth ratio in the single-flume experiments was rather low (around 1.0), the model is further assessed in a field confluence of the Sava and Danube Rivers, whose channels have B/h ≈ 20. Besides, all morphological features characteristic for alluvial river confluences are present in this confluence: the bend in a tributary, elevated bed of the tributary channel and a scour hole in the PCC. Confluence of the Sava and Danube Rivers in Belgrade, Serbia is shown in Figure 3. Only the upstream confluence was subject of the study6. Moving vessel approach was chosen due to heavy traffic toward and from the Belgrade Passengers’ Port, situated at this river section. Five equidistant cross-sections in the PCC (Fig. 3b) and one cross-section in each branch of the Belgrade river network were covered with the velocity/discharge moving vessel ADCP (Acoustic Doppler Current Profiler) measurements. Summary of the confluence site characteristics is given in Figure 3d and the measured discharge distribution together with the recorded water stage in Table 1. Five transects were made in each of the five PCC cross-sections. Velocity profiles for the u, v and w velocity components were obtained after averaging ADCP instantaneous velocity profiles from the five transects.

3 NUMERICAL MODELLING

The SSIIM2 model7, applied in this paper, is a 3D finite-volume model that solves Reynolds-averaged Navier-Stokes equations using the two-equation turbulence model closure. The model is based on the assumption of hydrostatic pressure distribution. Only results pertaining to the standard

Dejana Đorđević

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Figure 1: a) Plan view of the Shumate’s laboratory confluence; b) measuring cross-sections;

c) distribution of the measuring points within the cross-section (Shumate8)

a) concordant beds (CB)confluence

b) discordant beds (DB)confluence

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Figure 2: Biron et al.’s a) concordant and b) discordant beds confluences9, 10;

c) distribution of the measuring verticals; d) computational domain; e) detail of the computational grid

the Danube River

( ain channel)

m

the Danube River

(econdary channel)

s

Great Island

City ofBelgrade

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the Danube River(secondary channel)

the Sava R.(main river)

Figure 3: Confluence of the Sava and Danube Rivers: a) plan view, b) detail of the computational grid with the positions of the five cross-sections in the PCC, c) section through the tributary channel showing the difference in

bed elevations between the two combining channels; d) confluence site characteristics.

River B [ m ] α [ o ]

the Sava R. (upstream of the confluence) ~ 290

secondary chnl. of the Danube R. (tributary) 275

the Sava R. (downstream of the confluence) ~ 290

78

c) d)

А

А

Dejana Đorđević

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ΔZT* QT QMR ZT ZMR ZPCCExample No.

Description [m] [m3/s] [m.a.s.l]

Biron et al.’s CB confluence 0.00 0.0031 0.0025 0.16 0.16 0.16 2 Biron et al.’s DB confluence 0.03 0.0028 0.0025 0.13 0.16 0.16

3 Sava and Danube R. confluence ~10 325 930 70.4 70.4 70.4 * ΔZT - difference in bed elevations between the tributary and main channels, ZT, ZMR and ZPCC – water stages in the tributary, main-river and post-confluence channels.

Table 1 : Hydraulic conditions in Biron et al.’s experiments and in the confluence of the Sava and Danube Rivers during field measurements

k-ε model are presented in the paper, as this turbulence model provided the most satisfactory agree-ment with the measurements6.

The governing equations are solved on a 3D orthogonal/non-orthogonal unstructured, multiblock grid, which is suitable for discretisation of the dendritic flow domains such as those found in river confluences. The coupling of the continuity and momentum equations in SSIIM2 is achieved using SIMPLE algorithm. Due to high pressure and velocity gradients in the confluence, the second-order upwind scheme is used to discretise convective terms in the momentum equations.

Numerical simulations in this study are based on the steady flow assumption. The choice is grounded on the fact that the flow in the three examples was steady and subcritical. Although some other 3D models, used in previous studies1- 4, use porosity approach to represent free-surface varia-tions, this option is not available in SSIIM2. In this model, the free-surface is represented with the rigid lid. Normal velocity component at the free-surface and at the outflow boundaries is calculated in SSIIM2 using symmetric boundary condition and the wall-law is used to define boundary conditions along solid boundaries. Constant fluxes are defined at inflow boundaries and constant depth is specified at the outflow cross-section.

The multiblock grid comprises of two blocks in each example. Block 1 covers the main and post-confluence channels, and block 2, the tributary channel. Both blocks are orthogonal structured grids in the first example – 90o confluence; the two blocks are non-orthogonal structured grids in the 30o confluences (Fig. 2e); in the field confluence the grids are unstructured and non-orthogonal (Fig. 3b). Upstream and downstream cross-sections in the first example coincide with the limits of the Shumate’s facility (Fig. 1), while in the remaining two cases (30o and field confluences) upstream boundaries in the tributary and the main channel are placed ten channel widths upstream of the bend and the confluence, respectively. Likewise, downstream boundary is placed ten channel widths downstream of the confluence. Such a positioning of the computational domain boundaries ensured no influence of the boundary conditions on the flow pattern in the CHZ.

The grid independence analyses have shown that the grid independent solutions are obtained for the multi-block grids with the following dimensions: 1) 839×38×21 in block 1 and 183×38×21 in block 2 for the Shumate’s 90o confluence; 2) 493×31×33 in block 1 for both CB and DB Biron et al.’s 30o confluences, 291×17×33 in block 2 for the CB confluence and 291×17×26 for the DB confluence; 3) 201×31×11 in block 1 and 229×26×11 in block 2 for the field confluence. The first digit stands for the grid size in the downstream direction, second digit for the size in the lateral and the third digit for the size in the vertical direction.

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4 MODEL ASSESSMENT

4.1 Example 1: Shumate’s 90o confluence

Comparison of the calculated and measured velocity magnitudes and distributions at the tributary entrance to the confluence shows satisfactory agreement for the two horizontal velocity components u and v. Discrepancies are less than 5% in the bottom 0.6h. Such a good agreement reflects itself in good predictions of the δ flow-angle distributions (δ = arc tg(v/u) – Fig. 4a), i.e. in good prediction of the horizontal momentum transfer from the tributary to the main canal. However, in the upper 0.4h discrepancies start to increase and in the subsurface 0.2h they reach 20% for the u-velocity, which explains under prediction of the δ-angle, especially close to the upstream junction corner (l ≤ 0.30Lu-d, Fig. 4a). As for the vertical velocity w, it should be noted that despite consistent magnitude under prediction (≈ 50%), the shape of the w-velocity distributions is captured well6, which explains good agreement between the measured and calculated ϕ-angle distributions (ϕ = arc tg(w/(u2+v2)1/2), Fig. 4b) in the bottom 0.6h. Again, greater discrepancies are observed close to the upstream junction corner for 0.2h < z < 0.5h.

Variations of the RZ length and width throughout the flow depth are shown in Figure 5c-d. It should be stressed that the size of RZ was not measured during the experiments. Thus, it was deduced from the measured vector fields (Fig. 5a). Since the closest measuring point was 5 cm away from the wall, the deduced RZ lengths should be taken as rough estimates. Fortunately, there were no problems in estimating RZ width, whose values are, thus, more reliable. Generally, the RZ width (Fig. 5d) is captured well, especially for z ≤ 0.25h. However, the length of the RZ is under predicted by 20%. This suggests that greater shear is developed in the simulated flow. Indeed, comparison of the u and v-velocity profiles for the verticals within the RZ (Figs. 6a and 6c – not all verticals are presented here) reveals that there is quite the opposite circulation within the simulated RZ than in the experimental one. Good agreement of the v-velocity profiles in the shear layer (y = 0.375BPCC – Fig. 6c) indicates that the extraction of the momentum from the main flow to the RZ is simulated correctly. In the maximal velocity zone (y > 0.50BPCC) u and v velocities are underestimated by 20%, but the shape of the velocity profiles is captured well. In addition to the opposite circulation within the RZ

Figure 4: Comparison of the measured and Figure 5: Comparison of the measured a) and calculated b) velocity calculated distributions of flow angles δ a) and vector fields; variations of the RZ length c) and width d) throughout ϕ b) at the tributary entrance to the confluence. the flow depth.

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Dejana Đorđević

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y BPCC/ = 0.875

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zh/

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c)

d)

Figure 6: Comparison of the measured and calculated velocity profiles in the post-confluence channel:

a)-b) u-velocity profiles, c)-d) v-velocity profiles and e)-f) w-velocity profiles.

on the horizontal plane, there is also opposite circulation in the cross-section – close to the wall the simulated w-velocity is directed upward, while in the experiments it is directed downward (Fig. 6e). In the shear layer situation is reverse. Outside the RZ (y > 0.50BPCC) w-velocity profiles are captured well.

4.2 Example 2: Biron et al.’s 30o confluences

Calculated and measured u and w velocity profiles for the CB confluence are presented in Figure 7a-d, and those for the DB confluence in Figure 7e-h. Although no RZ was formed in the Biron et al.’s

experiments due to small junction angle, deceleration of flow in the flow stagnation zone (y < 0.067BPCC) downstream of the downstream junction corner is not captured in neither of the experiments – CB or DB (Figs. 7a and 7e). The flow recovery zone starts at x ≈ 0.920 BPCC. From this section onward, the dis-crepancies between the profiles start to decrease. Similar effect is observed within a cross-section when moving away from the junction-side wall towards the shear layer and maximal velocity zone. In the max-

u [ cm/s ]

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Figure 7: Comparison of the measured and calculated velocity profiles in the post-confluence channel

for the CB confluence: a)-b) u-velocity profiles and c)-d) w-velocity profiles, and for the DB confluence e)-f) u-velocity profiles and g)-h) w-velocity profiles.

Dejana Đorđević

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imal velocity zone (y > 0.50BPCC) the two profiles match perfectly. The w-velocity magnitude is under predicted as in the Shumate’s confluence. The under prediction is greater in the CB confluence for which the measured w-velocity is an order of magnitude lower than in the DB confluence (Figs. 7c-d and 7g-h). The overall under prediction in the CB case is around 70%, while in the DB case it reduces to 45%. What is encouraging is that despite systematic under prediction of the w-velocity magnitude, the shape of the profiles is captured well both throughout the flow width and along the post-confluence canal.

4.3 Example 3: The Sava and Danube Rivers’ confluence Instantaneous u, v and w velocity profiles for all transects along with the corresponding averaged

profiles are, for illustration, presented only for the deepest vertical (Fig. 8a) in the cross-section No.1 (Fig. 3b). Due to turbulence of different scales, that develops in and downstream of the confluence, dis-persion of the instantaneous velocities around the averaged profile is rather high – 80% for the u-velocity and up to 200% in some bins for the v and w velocities. Nevertheless, agreement between the simulated, time-averaged velocity profiles and corresponding averaged profiles from the five transects is satisfactory.

In addition to the instantaneous velocity profiles, the accompanying software for the ADCP unit (WinRiver) can present depth-averaged horizontal velocity vectors (Vxy = (u2 + v2)1/2) along the boat tra-jectory. Strictly speaking, time-averaged vector field should not be compared to the instantaneous one. However, this comparison is made just to gain rough impression weather the model of time- averaged flow is capable to describe the depth-averaged field satisfactorily. To facilitate comparison with numerical simulations, only verticals that coincide with the computational grid nodes are extracted from the raw data. Depth-averaged measured and simulated Vxy vectors for the two cross-sections are presented in Figure 9. Visually, agreement of both vector magnitudes and vector orientation along the two transects is satisfactory. Investigations on how to use moving vessel data for model validation purposes in case when there are no possibilities to perform fixed-vessel measurements are under way.

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[ m/s ] Figure 8: Instantaneous, averaged and calculated velocity profiles in the deepest vertical a) of the cross-section No.1

(Fig.3b) in the post-confluence channel; b) u-velocity profiles, c) v-velocity profiles, and d) w-velocity profiles.

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Figure 9: Instantaneous and calculated horizontal velocity vectors along the boat trajectory for the cross-sections a) No.2 and

b) No.3 in the post-confluence channel (Fig.3b).

Dejana Đorđević

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5 CONCLUSIONS

Detailed validation of the 3D finite-volume model SSIIM2 with the experimental and field data led to the following conclusions.

• Although a 3D model based on the hydrostatic pressure distribution captures the shape of the velocity profiles correctly, vertical velocity magnitude is substantially under predicted (more than 45%). This under prediction along with the pronounced streamline curvature indicates that it might be better to use a model based on non-hydrostatic pressure distribution in confluence hydrodynamics modelling.

• Transfer of the momentum from the tributary to the main river is described satisfactorily using the 3D model with the k-ε-type turbulence model closure. Therefore, variation of the recirculation zone width throughout the flow depth is predicted correctly. However, the model with the two-equation turbulence model closure fails to describe circulation within the recirculation zone properly. Consequently, the length of the RZ zone is under predicted.

REFERENCES [1] K.F. Bradbrook, P. Biron, S.N. Lane, K.S. Richards and A.G. Roy, “Investigation of controls on

secondary circulation in a simple confluence geometry using a three-dimensional numerical model”, Hydrological Processes, 12: 1371-1396 (1998).

[2] K.F. Bradbrook, S.N. Lane and K.S. Richards, “Numerical simulation of the three-dimensional, time-averaged flow structure at river channel confluences”, Water Resour. Res., 36(9): 2731-2746 (2000).

[3] K.F. Bradbrook, S.N. Lane, K.S. Richards, P.M. Biron and A.G. Roy, “Role of bed discordance at asymmetrical river confluences”, J. Hydraul. Eng. ASCE, 127(5): 351-368 (2001).

[4] J. Huang, L. J. Weber and Y. G. Lai, “Three-dimensional study of flows in open-channel junctions”, J. Hydraul. Engineering, ASCE, 128(3): 268-280 (2002).

[5] D. Đorđević and P.M. Biron, “Role of upstream planform curvature at asymmetrical confluences – laboratory experiment revisited”, Proc. 4th Int. Conference on Fluvial Hydraulics – River Flow 2008, Cesme 3: 2277-2286 (2008).

[6] D. Đorđević, Numerical investigation of the river confluence hydrodynamics, Unpublished PhD Dissertation, University of Belgrade, Belgrade, 382p (2010).

[7] N.R. Olsen, CFD Algorithms for Hydraulic Engineering, Trondheim: The Norwegian University of Science and Technology (2000).

[8] E.D. Shumate, Experimental description of flow at an open-channel junction, Unpublished Master thesis, Univ. of Iowa, Iowa, 150 p (1998).

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